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Let μ be a nonnegative Radon measure on which satisfies μ(B(x,r)) ≤ Crⁿ for any and r > 0 and some positive constants C and n ∈ (0,d]. In this paper, some weighted norm inequalities with weights of Muckenhoupt type are obtained for maximal singular integral operators with such a measure μ, via certain weighted estimates with weights of Muckenhoupt type involving the John-Strömberg maximal operator and the John-Strömberg sharp maximal operator, where ϱ,p ∈ [1,∞).
A weighted theory describing Morrey boundedness of fractional integral operators and fractional maximal operators is developed. A new class of weights adapted to Morrey spaces is proposed and a passage to the multilinear cases is covered.
In this paper we establish weighted norm inequalities for singular integral operators with kernel satisfying a variant of the classical Hörmander's condition.
Let X be a homogeneous space and let E be a UMD Banach space with a normalized unconditional basis . Given an operator T from to L¹(X), we consider the vector-valued extension T̃ of T given by . We prove a weighted integral inequality for the vector-valued extension of the Hardy-Littlewood maximal operator and a weighted Fefferman-Stein inequality between the vector-valued extensions of the Hardy-Littlewood and the sharp maximal operators, in the context of Orlicz spaces. We give sufficient...
Necessary and sufficient conditions are given for the Hardy-Littlewood maximal operator to be bounded on a weighted Orlicz space when the complementary Young function satisfies . Such a growth condition is shown to be necessary for any weighted integral inequality to occur. Weak-type conditions are also investigated.
We propose a concept of weighted pseudo almost automorphic functions on almost periodic time scales and study some important properties of weighted pseudo almost automorphic functions on almost periodic time scales. As applications, we obtain the conditions for the existence of weighted pseudo almost automorphic mild solutions to a class of semilinear dynamic equations on almost periodic time scales.
We establish weighted sharp maximal function inequalities for a linear operator associated to a singular integral operator with non-smooth kernel. As an application, we obtain the boundedness of a commutator on weighted Lebesgue spaces.
We give a weighted version of the Sobolev-Lieb-Thirring inequality for suborthonormal functions. In the proof of our result we use phi-transform of Frazier-Jawerth.
Let be the Ariõ-Muckenhoupt weight class which controls the weighted -norm inequalities for the Hardy operator on non-increasing functions. We replace the constant p by a function p(x) and examine the associated -norm inequalities of the Hardy operator.
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